Coefficients of inbreeding and homozygosity in recurrent selection: The case of m linked loci

Summary Methods of calculating the coefficients of inbreeding and homozygosity in a finite population undergoing recurrent selection (self-select-intercross in succeeding generations) are investigated for the case of m linked loci and effective directional selection. These coefficients are derived in terms of vectors whose components reflect the various possible patterns of genes being identical at a given stage of the recurrent selection breeding program.For the case of two linked loci the progress of the panmictic index and/or the index of total heterozygosity through twenty-five cycles of recurrent selection is traced by means of computer-simulated populations ranging in sizes from ten through one hundred, assuming varying recombination probabilities, and assuming both minimum and maximum inbreeding selection patterns.Results indicate that the coefficient of relationship in the source population is extremely important in tracing the progress of the degree of inbreeding and/or total homozygosity, that linkage plays a major role in promoting heterozygosity in a recurrent selection system, and that careful intercrossing rather than random mating in alternate generations of the recurrent selection cycle is important in promoting maximum heterozygosity in the selected population. In the simulated populations the effect of small population sizes is observed and, in general, indications are that unless more than five complete recurrent cycles are contemplated, increasing the population size results in only relatively minor increases in panmixia, especially when linked loci are involved in the selected trait and when care is taken to avoid a maximum inbreeding selection pattern.